Coalescent theory is a branch of mathematical evolutionary theory that began as recently as the early 80's. Compared to previous methods like simulation of the Wright-Fisher model, its methods provide a computationally efficient statistical analysis of genetic samples. Because of the HapMap Project, which is elaborating a haplotype map of humans, it has implications for the understanding of genome-wide associations studies, and thereby the determination of single nucleotide polymorphisms (SNPs) that contribute to human disease. Active areas of recent research in coalescent theory include the determination of human recombination rates, and in particular the prediction of so-called recombination hot-spots. The location of recombination hot-spots is critical to interpreting linkage disequilibrium, which influences the interpretation of data from genome-wide association studies. Dr. Tewari has developed a Java framework for analyzing coalescent recursions. Drs. Szekely, Czabarka, and Spouge have a draft manuscript of new combinatorial interpretations of coalescent results. Drs. Tewari and Spouge also have discovered a general means of accelerating coalescent computations and are exploring its implications.